{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ML_in_Finance_QLBS_Option_Pricing\n",
    "# Author: Igor Halperin\n",
    "# Version: 1.0 (06.05.2020)\n",
    "# License: MIT\n",
    "# Email: matthew.dixon@iit.edu\n",
    "# Notes: tested on Mac OS X with Python 3.6.9 and the following packages:\n",
    "# matplotlib=3.1.3, numpy=1.18.1, scipy=1.4.1, pandas=1.0.4\n",
    "# Citation: Please cite the following reference if this notebook is used for research purposes:\n",
    "# Bilokon P., Dixon M.F. and Halperin I., Machine Learning in Finance: From Theory to Practice, Springer Graduate textbook Series, 2020."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import norm\n",
    "import random\n",
    "import time\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameters for MC simulation of stock prices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Begin by simulating stock price dynamics under GBM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "S0 = 100      # initial stock price\n",
    "mu = 0.05     # drift\n",
    "sigma = 0.15  # volatility\n",
    "r = 0.03      # risk-free rate\n",
    "\n",
    "M = 1         # maturity\n",
    "T = 24        # number of time steps\n",
    "\n",
    "N_MC = 1000    # number of paths\n",
    "\n",
    "delta_t = M / T                # time interval\n",
    "gamma = np.exp(- r * delta_t)  # discount factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GBM Simulation\n",
    "Simulate $N_{MC}$ stock price sample paths with $T$ steps by the classical GBM formula.\n",
    "\n",
    "$$dS_t=\\mu S_tdt+\\sigma S_tdW_t\\quad\\quad S_{t+1}=S_te^{\\left(\\mu-\\frac{1}{2}\\sigma^2\\right)\\Delta t+\\sigma\\sqrt{\\Delta t}Z}$$\n",
    "\n",
    "where $Z$ is a standard normal random variable.\n",
    "\n",
    "Based on simulated stock price $S_t$ paths, compute state variable $X_t$ by the following relation.\n",
    "\n",
    "$$X_t=-\\left(\\mu-\\frac{1}{2}\\sigma^2\\right)t\\Delta t+\\log S_t$$\n",
    "\n",
    "Also compute\n",
    "\n",
    "$$\\Delta S_t=S_{t+1}-e^{r\\Delta t}S_t\\quad\\quad \\Delta\\hat{S}_t=\\Delta S_t-\\Delta\\bar{S}_t\\quad\\quad t=0,...,T-1$$\n",
    "\n",
    "where $\\Delta\\bar{S}_t$ is the sample mean of all values of $\\Delta S_t$.\n",
    "\n",
    "Plots of 5 stock price $S_t$ and state variable $X_t$ paths are shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Time Cost: 0.19748210906982422 seconds\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make two datasets \n",
    "# the second dataset will be needed below for Double Q-Learning\n",
    "\n",
    "starttime = time.time()\n",
    "\n",
    "# stock price\n",
    "S = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "S.loc[:,0] = S0\n",
    "\n",
    "S_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "S_1.loc[:,0] = S0\n",
    "\n",
    "# standard normal random numbers\n",
    "RN = pd.DataFrame(np.random.randn(N_MC,T), index=range(1, N_MC+1), columns=range(1, T+1))\n",
    "RN_1 = pd.DataFrame(np.random.randn(N_MC,T), index=range(1, N_MC+1), columns=range(1, T+1))\n",
    "\n",
    "for t in range(1, T+1):\n",
    "    S.loc[:,t] = S.loc[:,t-1] * np.exp((mu - 1/2 * sigma**2) * delta_t + sigma * np.sqrt(delta_t) * RN.loc[:,t])\n",
    "    S_1.loc[:,t] = S_1.loc[:,t-1] * np.exp((mu - 1/2 * sigma**2) * delta_t + sigma * np.sqrt(delta_t) * RN_1.loc[:,t])\n",
    "\n",
    "delta_S = S.loc[:,1:T].values - np.exp(r * delta_t) * S.loc[:,0:T-1]\n",
    "delta_S_hat = delta_S.apply(lambda x: x - np.mean(x), axis=0)\n",
    "\n",
    "delta_S_1 = S_1.loc[:,1:T].values - np.exp(r * delta_t) * S_1.loc[:,0:T-1]\n",
    "delta_S_hat_1 = delta_S_1.apply(lambda x: x - np.mean(x), axis=0)\n",
    "\n",
    "# state variable\n",
    "X = - (mu - 1/2 * sigma**2) * np.arange(T+1) * delta_t + np.log(S)   # delta_t here is due to their conventions\n",
    "X_1 = - (mu - 1/2 * sigma**2) * np.arange(T+1) * delta_t + np.log(S_1) \n",
    "\n",
    "endtime = time.time()\n",
    "print('\\nTime Cost:', endtime - starttime, 'seconds')\n",
    "\n",
    "# plot 10 paths\n",
    "step_size = N_MC // 10\n",
    "idx_plot = np.arange(step_size, N_MC, step_size)\n",
    "plt.plot(S.T.iloc[:, idx_plot])\n",
    "plt.xlabel('Time Steps')\n",
    "plt.title('Stock Price Sample Paths')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(X.T.iloc[:, idx_plot])\n",
    "plt.xlabel('Time Steps')\n",
    "plt.ylabel('State Variable');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define function *terminal_payoff* to compute the terminal payoff of a European put option.\n",
    "\n",
    "$$H_T\\left(S_T\\right)=\\max\\left(K-S_T,0\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def terminal_payoff(ST, K):\n",
    "    # ST   final stock price\n",
    "    # K    strike\n",
    "    payoff = max(K - ST, 0)\n",
    "    return payoff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Define spline basis functions  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X.shape =  (1000, 25)\n",
      "X_min, X_max =  4.044328505849859 5.059985690708386\n",
      "Number of points k =  17\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import bspline\n",
    "import bspline.splinelab as splinelab\n",
    "\n",
    "X_min = np.min(np.min(X))\n",
    "X_max = np.max(np.max(X))\n",
    "\n",
    "print('X.shape = ', X.shape)\n",
    "print('X_min, X_max = ', X_min, X_max)\n",
    "\n",
    "p = 4 # order of spline (as-is; 3: cubic, 4: B-spline?)\n",
    "ncolloc = 12\n",
    "\n",
    "tau = np.linspace(X_min, X_max, ncolloc)  # These are the sites to which we would like to interpolate\n",
    "\n",
    "# k is a knot vector that adds endpoints repeats as appropriate for a spline of order p\n",
    "# To get meaninful results, one should have ncolloc >= p+1\n",
    "k = splinelab.aptknt(tau, p) \n",
    "                             \n",
    "# Spline basis of order p on knots k\n",
    "basis = bspline.Bspline(k, p)        \n",
    "f = plt.figure()\n",
    "\n",
    "print('Number of points k = ', len(k))\n",
    "basis.plot()\n",
    "\n",
    "plt.savefig('Basis_functions.png', dpi=600)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bspline.bspline.Bspline"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(basis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 25)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.values.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Make data matrices with feature values\n",
    "\n",
    "\"Features\" here are the values of basis functions at data points\n",
    "The outputs are 3D arrays of dimensions num_tSteps x num_MC x num_basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "num_basis =  12\n",
      "dim data_mat_t =  (25, 1000, 12)\n",
      "Computational time: 8.037918090820312 seconds\n"
     ]
    }
   ],
   "source": [
    "num_t_steps = T + 1\n",
    "num_basis =  ncolloc \n",
    "\n",
    "data_mat_t = np.zeros((num_t_steps, N_MC,num_basis ))\n",
    "data_mat_t_1 = np.zeros((num_t_steps, N_MC,num_basis ))\n",
    "\n",
    "print('num_basis = ', num_basis)\n",
    "print('dim data_mat_t = ', data_mat_t.shape)\n",
    "\n",
    "t_0 = time.time()\n",
    "\n",
    "# fill it \n",
    "for i in np.arange(num_t_steps):\n",
    "    x = X.values[:,i]\n",
    "    x_1 = X_1.values[:,i]\n",
    "    data_mat_t[i,:,:] = np.array([ basis(i) for i in x ])\n",
    "    data_mat_t_1[i,:,:] = np.array([ basis(i) for i in x_1 ])\n",
    "    \n",
    "t_end = time.time()\n",
    "print('Computational time:', t_end - t_0, 'seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# save these data matrices for future re-use\n",
    "np.save('data_mat_m=r_A_%d' % N_MC, data_mat_t)\n",
    "np.save('data_mat_m=r_B_%d' % N_MC, data_mat_t_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(25, 1000, 12)\n",
      "17\n"
     ]
    }
   ],
   "source": [
    "print(data_mat_t.shape) # shape: num_steps x N_MC x num_basis\n",
    "print(len(k))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic Programming solution for QLBS \n",
    "\n",
    "The MDP problem in this case is to solve the following Bellman optimality equation for the action-value function.\n",
    "\n",
    "$$Q_t^\\star\\left(x,a\\right)=\\mathbb{E}_t\\left[R_t\\left(X_t,a_t,X_{t+1}\\right)+\\gamma\\max_{a_{t+1}\\in\\mathcal{A}}Q_{t+1}^\\star\\left(X_{t+1},a_{t+1}\\right)\\space|\\space X_t=x,a_t=a\\right],\\space\\space t=0,...,T-1,\\quad\\gamma=e^{-r\\Delta t}$$\n",
    "\n",
    "where $R_t\\left(X_t,a_t,X_{t+1}\\right)$ is the one-step time-dependent random reward and $a_t\\left(X_t\\right)$ is the action (hedge).\n",
    "\n",
    "Detailed steps of solving this equation by Dynamic Programming are illustrated below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this set of basis functions $\\left\\{\\Phi_n\\left(X_t^k\\right)\\right\\}_{n=1}^N$, expand the optimal action (hedge) $a_t^\\star\\left(X_t\\right)$ and optimal Q-function $Q_t^\\star\\left(X_t,a_t^\\star\\right)$ in basis functions with time-dependent coefficients.\n",
    "$$a_t^\\star\\left(X_t\\right)=\\sum_n^N{\\phi_{nt}\\Phi_n\\left(X_t\\right)}\\quad\\quad Q_t^\\star\\left(X_t,a_t^\\star\\right)=\\sum_n^N{\\omega_{nt}\\Phi_n\\left(X_t\\right)}$$\n",
    "\n",
    "Coefficients $\\phi_{nt}$ and $\\omega_{nt}$ are computed recursively backward in time for $t=T−1,...,0$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coefficients for expansions of the optimal action $a_t^\\star\\left(X_t\\right)$ are solved by\n",
    "\n",
    "$$\\phi_t=\\mathbf A_t^{-1}\\mathbf B_t$$\n",
    "\n",
    "where $\\mathbf A_t$ and $\\mathbf B_t$ are matrix and vector respectively with elements given by\n",
    "\n",
    "$$A_{nm}^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Phi_n\\left(X_t^k\\right)\\Phi_m\\left(X_t^k\\right)\\left(\\Delta\\hat{S}_t^k\\right)^2}\\quad\\quad B_n^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Phi_n\\left(X_t^k\\right)\\left[\\hat\\Pi_{t+1}^k\\Delta\\hat{S}_t^k+\\frac{1}{2\\gamma\\lambda}\\Delta S_t^k\\right]}$$\n",
    "\n",
    "Define function *function_A* and *function_B* to compute the value of matrix $\\mathbf A_t$ and vector $\\mathbf B_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the option strike and risk aversion parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "risk_lambda = 0.001 # risk aversion parameter\n",
    "\n",
    "K = 100 # strike  \n",
    "\n",
    "# Note that we set coef=0 below in function function_B_vec. This corresponds to a pure risk-based hedging"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# functions to compute optimal hedges\n",
    "def function_A_vec(t,delta_S_hat,data_mat,reg_param):\n",
    "    # Compute the matrix A_{nm} from Eq. (52) (with a regularization!)\n",
    "    X_mat = data_mat_t[t,:,:]\n",
    "    num_basis_funcs = X_mat.shape[1]\n",
    "    this_dS = delta_S_hat.loc[:,t].values\n",
    "    hat_dS2 = (this_dS**2).reshape(-1,1)    \n",
    "    A_mat = np.dot(X_mat.T, X_mat * hat_dS2) + reg_param * np.eye(num_basis_funcs)\n",
    "    return A_mat\n",
    "        \n",
    "def function_B_vec(t, Pi_hat, delta_S=delta_S, delta_S_hat=delta_S_hat, S=S, data_mat=data_mat_t,\n",
    "                  gamma=gamma,risk_lambda=risk_lambda):\n",
    "    # coef = 1.0/(2 * gamma * risk_lambda)\n",
    "    # override it by zero to have pure risk hedge\n",
    "    coef = 0\n",
    "    tmp =  Pi_hat.loc[:,t+1] * delta_S_hat.loc[:,t] + coef * (np.exp(mu*delta_t) - np.exp(r*delta_t))* S.loc[:,t]\n",
    "    X_mat = data_mat_t[t,:,:]  # matrix of dimension N_MC x num_basis\n",
    "    \n",
    "    B = np.dot(X_mat.T, tmp)    \n",
    "    return B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute optimal hedge and portfolio value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call *function_A* and *function_B* for $t=T-1,...,0$ together with basis function $\\Phi_n\\left(X_t\\right)$ to compute optimal action $a_t^\\star\\left(X_t\\right)=\\sum_n^N{\\phi_{nt}\\Phi_n\\left(X_t\\right)}$ backward recursively with terminal condition $a_T^\\star\\left(X_T\\right)=0$.\n",
    "\n",
    "Once the optimal hedge $a_t^\\star\\left(X_t\\right)$ is computed, the portfolio value $\\Pi_t$ could also be computed backward recursively by \n",
    "\n",
    "$$\\Pi_t=\\gamma\\left[\\Pi_{t+1}-a_t^\\star\\Delta S_t\\right]\\quad t=T-1,...,0$$\n",
    "\n",
    "together with the terminal condition $\\Pi_T=H_T\\left(S_T\\right)=\\max\\left(K-S_T,0\\right)$ for a European put option.\n",
    "\n",
    "Also compute $\\hat{\\Pi}_t=\\Pi_t-\\bar{\\Pi}_t$, where $\\bar{\\Pi}_t$ is the sample mean of all values of $\\Pi_t$.\n",
    "\n",
    "Plots of 5 optimal hedge $a_t^\\star$ and portfolio value $\\Pi_t$ paths are shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computational time: 0.359637975692749 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "starttime = time.time()\n",
    "\n",
    "# portfolio value\n",
    "Pi = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi.iloc[:,-1] = S.iloc[:,-1].apply(lambda x: terminal_payoff(x, K))\n",
    "\n",
    "Pi_hat = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi_hat.iloc[:,-1] = Pi.iloc[:,-1] - np.mean(Pi.iloc[:,-1])\n",
    "\n",
    "# optimal hedge\n",
    "a = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "a.iloc[:,-1] = 0\n",
    "\n",
    "# twin variables for the second dataset\n",
    "# portfolio value\n",
    "Pi_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi_1.iloc[:,-1] = S_1.iloc[:,-1].apply(lambda x: terminal_payoff(x, K))\n",
    "\n",
    "Pi_hat_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi_hat_1.iloc[:,-1] = Pi_1.iloc[:,-1] - np.mean(Pi_1.iloc[:,-1])\n",
    "\n",
    "# optimal hedge\n",
    "a_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "a_1.iloc[:,-1] = 0\n",
    "\n",
    "reg_param = 1e-3\n",
    "\n",
    "for t in range(T-1, -1, -1):\n",
    "    A_mat = function_A_vec(t, delta_S_hat, data_mat_t, reg_param)\n",
    "    B_vec = function_B_vec(t, Pi_hat)\n",
    "\n",
    "    # print ('t =  A_mat.shape = B_vec.shape = ', t, A_mat.shape, B_vec.shape)\n",
    "    phi = np.dot(np.linalg.inv(A_mat), B_vec)\n",
    "\n",
    "    a.loc[:,t] = np.dot(data_mat_t[t,:,:],phi)\n",
    "    Pi.loc[:,t] = gamma * (Pi.loc[:,t+1] - a.loc[:,t] * delta_S.loc[:,t])\n",
    "    Pi_hat.loc[:,t] = Pi.loc[:,t] - np.mean(Pi.loc[:,t])\n",
    "\n",
    "    # and the same for the twin dataset:\n",
    "    A_mat_1 = function_A_vec(t,delta_S_hat_1,data_mat_t_1,reg_param)\n",
    "    B_vec_1 = function_B_vec(t, Pi_hat_1)\n",
    "    phi_1 = np.dot(np.linalg.inv(A_mat_1), B_vec_1)\n",
    "    a_1.loc[:,t] = np.dot(data_mat_t_1[t,:,:],phi_1)\n",
    "    Pi_1.loc[:,t] = gamma * (Pi_1.loc[:,t+1] - a_1.loc[:,t] * delta_S_1.loc[:,t])\n",
    "    Pi_hat_1.loc[:,t] = Pi_1.loc[:,t] - np.mean(Pi_1.loc[:,t])\n",
    "\n",
    "a = a.astype('float')\n",
    "Pi = Pi.astype('float')\n",
    "Pi_hat = Pi_hat.astype('float')\n",
    "\n",
    "a_1 = a_1.astype('float')\n",
    "Pi_1 = Pi_1.astype('float')\n",
    "Pi_hat_1 = Pi_hat_1.astype('float')\n",
    "\n",
    "endtime = time.time()\n",
    "print('Computational time:', endtime - starttime, 'seconds')\n",
    "\n",
    "# plot 10 paths\n",
    "plt.plot(a.T.iloc[:,idx_plot])\n",
    "plt.xlabel('Time Steps')\n",
    "plt.title('Optimal Hedge')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(Pi.T.iloc[:,idx_plot])\n",
    "plt.xlabel('Time Steps')\n",
    "plt.title('Portfolio Value');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the optimal hedge $a_t^\\star$ and portfolio value $\\Pi_t$ are all computed, the reward function $R_t\\left(X_t,a_t,X_{t+1}\\right)$ could then be computed by\n",
    "\n",
    "$$R_t\\left(X_t,a_t,X_{t+1}\\right)=\\gamma a_t\\Delta S_t-\\lambda Var\\left[\\Pi_t\\space|\\space\\mathcal F_t\\right]\\quad t=0,...,T-1$$\n",
    "\n",
    "with terminal condition $R_T=-\\lambda Var\\left[\\Pi_T\\right]$.\n",
    "\n",
    "Plot of 5 reward function $R_t$ paths is shown below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute the optimal Q-function with the DP approach "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coefficients for expansions of the optimal Q-function $Q_t^\\star\\left(X_t,a_t^\\star\\right)$ are solved by\n",
    "\n",
    "$$\\omega_t=\\mathbf C_t^{-1}\\mathbf D_t$$\n",
    "\n",
    "where $\\mathbf C_t$ and $\\mathbf D_t$ are matrix and vector respectively with elements given by\n",
    "\n",
    "$$C_{nm}^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Phi_n\\left(X_t^k\\right)\\Phi_m\\left(X_t^k\\right)}\\quad\\quad D_n^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Phi_n\\left(X_t^k\\right)\\left(R_t\\left(X_t,a_t^\\star,X_{t+1}\\right)+\\gamma\\max_{a_{t+1}\\in\\mathcal{A}}Q_{t+1}^\\star\\left(X_{t+1},a_{t+1}\\right)\\right)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define function *function_C* and *function_D* to compute the value of matrix $\\mathbf C_t$ and vector $\\mathbf D_t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def function_C_vec(t,data_mat_t,reg_param):\n",
    "    # Compute the matrix A_{nm} from Eq. (52) (with a regularization!)\n",
    "    X_mat = data_mat_t[t,:,:]\n",
    "    num_basis_funcs = X_mat.shape[1]    \n",
    "    C_mat = np.dot(X_mat.T, X_mat) + reg_param * np.eye(num_basis_funcs)\n",
    "    return C_mat\n",
    "\n",
    "def function_D_vec(t, Q, R, data_mat_t, gamma=gamma):\n",
    "    X_mat = data_mat_t[t,:,:]\n",
    "    tmp = R.loc[:,t] + gamma * Q.loc[:,t+1]  # note that the second argument in Q is t+1 !\n",
    "    D = np.dot(X_mat.T, tmp.values)\n",
    "    return D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call *function_C* and *function_D* for $t=T-1,...,0$ together with basis function $\\Phi_n\\left(X_t\\right)$ to compute optimal action Q-function $Q_t^\\star\\left(X_t,a_t^\\star\\right)=\\sum_n^N{\\omega_{nt}\\Phi_n\\left(X_t\\right)}$ backward recursively with terminal condition $Q_T^\\star\\left(X_T,a_T=0\\right)=-\\Pi_T\\left(X_T\\right)-\\lambda Var\\left[\\Pi_T\\left(X_T\\right)\\right]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the QLBS price to European put price given by Black-Sholes formula.\n",
    "\n",
    "$$C_t^{\\left(BS\\right)}=Ke^{-r\\left(T-t\\right)}\\mathcal N\\left(-d_2\\right)-S_t\\mathcal N\\left(-d_1\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The Black-Scholes prices\n",
    "def bs_put(t, S0=S0, K=K, r=r, sigma=sigma, T=M):\n",
    "    d1 = (np.log(S0/K) + (r + 1/2 * sigma**2) * (T-t)) / sigma / np.sqrt(T-t)\n",
    "    d2 = (np.log(S0/K) + (r - 1/2 * sigma**2) * (T-t)) / sigma / np.sqrt(T-t)\n",
    "    price = K * np.exp(-r * (T-t)) * norm.cdf(-d2) - S0 * norm.cdf(-d1)\n",
    "    return price\n",
    "\n",
    "def bs_call(t, S0=S0, K=K, r=r, sigma=sigma, T=M):\n",
    "    d1 = (np.log(S0/K) + (r + 1/2 * sigma**2) * (T-t)) / sigma / np.sqrt(T-t)\n",
    "    d2 = (np.log(S0/K) + (r - 1/2 * sigma**2) * (T-t)) / sigma / np.sqrt(T-t)\n",
    "    price = S0 * norm.cdf(d1) - K * np.exp(-r * (T-t)) * norm.cdf(d2)\n",
    "    return price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hedging and Pricing with Reinforcement Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement a batch-mode off-policy model-free Q-Learning by Fitted Q-Iteration. The only data available is given by a set of $N_{MC}$ paths for the underlying state variable $X_t$, hedge position $a_t$, instantaneous reward $R_t$ and the next-time value $X_{t+1}$.\n",
    "\n",
    "$$\\mathcal F_t^k=\\left\\{\\left(X_t^k,a_t^k,R_t^k,X_{t+1}^k\\right)\\right\\}_{t=0}^{T-1}\\quad k=1,...,N_{MC}$$\n",
    "\n",
    "Detailed steps of solving the Bellman optimalty equation by Reinforcement Learning are illustrated below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Expand Q-function in basis functions with time-dependent coefficients parametrized by a matrix $\\mathbf W_t$.\n",
    "\n",
    "$$Q_t^\\star\\left(X_t,a_t\\right)=\\mathbf A_t^T\\mathbf W_t\\Phi\\left(X_t\\right)=\\mathbf A_t^T\\mathbf U_W\\left(t,X_t\\right)=\\vec{W}_t^T \\vec{\\Psi}\\left(X_t,a_t\\right)$$\n",
    "\n",
    "$$\\mathbf A_t=\\left(\\begin{matrix}1\\\\a_t\\\\\\frac{1}{2}a_t^2\\end{matrix}\\right)\\quad\\mathbf U_W\\left(t,X_t\\right)=\\mathbf W_t\\Phi\\left(X_t\\right)$$\n",
    "\n",
    "where $\\vec{W}_t$ is obtained by concatenating columns of matrix $\\mathbf W_t$ while \n",
    "$ vec \\left( {\\bf \\Psi} \\left(X_t,a_t \\right) \\right) = \n",
    "  vec \\, \\left( {\\bf A}_t  \\otimes {\\bf \\Phi}^T(X) \\right) $ stands for \n",
    "a vector obtained by concatenating columns of the outer product of vectors $ {\\bf A}_t $ and $ {\\bf \\Phi}(X) $.\n",
    "\n",
    "Compute vector $\\mathbf A_t$ then compute $\\vec\\Psi\\left(X_t,a_t\\right)$ for each $X_t^k$ and store in a dictionary with key path and time $\\left[k,t\\right]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 25)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# part of DP solution\n",
    "a.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make off-policy data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done!\n"
     ]
    }
   ],
   "source": [
    "# disturbance level eta: Each action is multiplied by a uniform r.v. in the interval [1-eta, 1 + eta]\n",
    "eta = 0.1\n",
    "reg_param = 1e-3\n",
    "\n",
    "a_op = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "a_op.iloc[:,-1] = 0\n",
    "\n",
    "a_op_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "a_op_1.iloc[:,-1] = 0\n",
    "\n",
    "# also make portfolios and rewards\n",
    "# portfolio value\n",
    "Pi_op = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi_op.iloc[:,-1] = S.iloc[:,-1].apply(lambda x: terminal_payoff(x, K))\n",
    "\n",
    "Pi_op_hat = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi_op_hat.iloc[:,-1] = Pi_op.iloc[:,-1] - np.mean(Pi_op.iloc[:,-1])\n",
    "\n",
    "Pi_op_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi_op_1.iloc[:,-1] = S_1.iloc[:,-1].apply(lambda x: terminal_payoff(x, K))\n",
    "\n",
    "Pi_op_hat_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Pi_op_hat_1.iloc[:,-1] = Pi_op_1.iloc[:,-1] - np.mean(Pi_op_1.iloc[:,-1])\n",
    "\n",
    "# reward function\n",
    "R_op = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "R_op.iloc[:,-1] = - risk_lambda * np.var(Pi_op.iloc[:,-1])\n",
    "\n",
    "R_op_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "R_op_1.iloc[:,-1] = - risk_lambda * np.var(Pi_op_1.iloc[:,-1])\n",
    "\n",
    "# The backward loop\n",
    "for t in range(T-1, -1, -1):\n",
    "    # 1. Compute the optimal policy, and write the result to a_op\n",
    "    A_mat = function_A_vec(t, delta_S_hat, data_mat_t, reg_param)\n",
    "    B_vec = function_B_vec(t, Pi_hat)\n",
    "    phi = np.dot(np.linalg.inv(A_mat), B_vec)\n",
    "    \n",
    "    A_mat_1 = function_A_vec(t, delta_S_hat_1, data_mat_t_1, reg_param)\n",
    "    B_vec_1 = function_B_vec(t, Pi_hat_1)\n",
    "    phi_1 = np.dot(np.linalg.inv(A_mat_1), B_vec_1)\n",
    "    \n",
    "    a_op.loc[:,t] = np.dot(data_mat_t[t,:,:],phi) \n",
    "    a_op_1.loc[:,t] = np.dot(data_mat_t_1[t,:,:],phi_1) \n",
    "     \n",
    "    # 2. Now disturb these values by a random noise\n",
    "    noise_factors = np.random.uniform(low=1-eta, high=1+eta, size=N_MC)\n",
    "    a_op.loc[:, t] = noise_factors * a_op.loc[:, t]\n",
    "    a_op_1.loc[:, t] = noise_factors * a_op_1.loc[:, t]\n",
    "    \n",
    "    # 3. Compute portfolio values corresponding to observed actions\n",
    "    Pi_op.loc[:,t] = gamma * (Pi_op.loc[:,t+1] - a_op.loc[:,t] * delta_S.loc[:,t])\n",
    "    Pi_op_hat.loc[:,t] = Pi_op.loc[:,t] - np.mean(Pi_op.loc[:,t])\n",
    "    Pi_op_1.loc[:,t] = gamma * (Pi_op_1.loc[:,t+1] - a_op_1.loc[:,t] * delta_S_1.loc[:,t])\n",
    "    Pi_op_hat_1.loc[:,t] = Pi_op_1.loc[:,t] - np.mean(Pi_op_1.loc[:,t])\n",
    "    \n",
    "    # compute rewards corrresponding to observed actions\n",
    "    R_op.loc[1:,t] = gamma * a_op.loc[1:,t] * delta_S.loc[1:,t] - risk_lambda * np.var(Pi_op.loc[1:,t])\n",
    "    R_op_1.loc[1:,t] = gamma * a_op_1.loc[1:,t] * delta_S_1.loc[1:,t] - risk_lambda * np.var(Pi_op_1.loc[1:,t])\n",
    "    \n",
    "print('done!')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Override on-policy data with off-policy data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = a_op.copy()\n",
    "a_1 = a_op_1.copy()\n",
    "\n",
    "Pi = Pi_op.copy()\n",
    "Pi_hat = Pi_op_hat.copy()\n",
    "Pi_1 = Pi_op_1.copy()\n",
    "Pi_hat_1 = Pi_op_hat_1.copy()\n",
    "\n",
    "R = R_op.copy()\n",
    "R_1 = R_op_1.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 1000, 25) (3, 1000, 25)\n"
     ]
    }
   ],
   "source": [
    "# make matrix A_t of shape (3 x num_MC x num_steps)\n",
    "\n",
    "num_MC = a.shape[0]\n",
    "a_1_1 = a.values.reshape((1,num_MC,25))\n",
    "\n",
    "a_1_2 = 0.5 * a_1_1**2\n",
    "ones_3d = np.ones((1,num_MC, 25))\n",
    "\n",
    "A_stack = np.vstack((ones_3d, a_1_1, a_1_2))\n",
    "\n",
    "# and the same for the second dataset:\n",
    "a_2_1 = a_1.values.reshape((1,num_MC,25))\n",
    "a_2_2 = 0.5 * a_2_1**2\n",
    "A_stack_1 = np.vstack((ones_3d, a_2_1, a_2_2))\n",
    "\n",
    "print(A_stack.shape, A_stack_1.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(25, 1000, 12)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_mat_t.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "aand a_1_1 shapes: (1000, 25) (1, 1000, 25)\n"
     ]
    }
   ],
   "source": [
    "print('a & a_1_1 shapes:', a.shape, a_1_1.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(12, 1000, 25)\n",
      "(36, 1000, 25) (36, 1000, 25)\n"
     ]
    }
   ],
   "source": [
    "data_mat_swap_idx = np.swapaxes(data_mat_t,0,2)\n",
    "data_mat_swap_idx_1 = np.swapaxes(data_mat_t_1,0,2)\n",
    "\n",
    "print(data_mat_swap_idx.shape) # (12, 10000, 25)\n",
    "\n",
    "# expand dimensions of matrices to multiply element-wise\n",
    "A_2 = np.expand_dims(A_stack, axis=1) # becomes (3,1,10000,25)\n",
    "data_mat_swap_idx = np.expand_dims(data_mat_swap_idx, axis=0)  # becomes (1,12,10000,25)\n",
    "\n",
    "Psi_mat = np.multiply(A_2, data_mat_swap_idx) # this is a matrix of size 3 x num_basis x num_MC x num_steps\n",
    "\n",
    "# now concatenate columns along the first dimension\n",
    "Psi_mat = Psi_mat.reshape(-1, N_MC, T+1, order='F')\n",
    "\n",
    "# the same for the twin dataset\n",
    "A_2_1 = np.expand_dims(A_stack_1, axis=1)\n",
    "data_mat_swap_idx_1 = np.expand_dims(data_mat_swap_idx_1, axis=0)\n",
    "\n",
    "Psi_mat_1 = np.multiply(A_2_1, data_mat_swap_idx_1) # this is a matrix of size 3 x num_basis x num_MC x num_steps\n",
    "\n",
    "# now concatenate columns along the first dimension\n",
    "Psi_mat_1 = Psi_mat_1.reshape(-1, N_MC, T+1, order='F')\n",
    "\n",
    "print(Psi_mat.shape, Psi_mat_1.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(36, 1, 1000, 25) (1, 36, 1000, 25)\n",
      "(36, 1, 1000, 25) (1, 36, 1000, 25)\n",
      "(36, 36, 25) (36, 36, 25)\n"
     ]
    }
   ],
   "source": [
    "# make matrix S_t \n",
    "\n",
    "Psi_1_aux = np.expand_dims(Psi_mat, axis=1)\n",
    "Psi_2_aux = np.expand_dims(Psi_mat, axis=0)\n",
    "print(Psi_1_aux.shape, Psi_2_aux.shape)\n",
    "\n",
    "S_t_mat = np.sum(np.multiply(Psi_1_aux, Psi_2_aux), axis=2) \n",
    "\n",
    "Psi_1_aux_1 = np.expand_dims(Psi_mat_1, axis=1)\n",
    "Psi_2_aux_1 = np.expand_dims(Psi_mat_1, axis=0)\n",
    "print(Psi_1_aux_1.shape, Psi_2_aux_1.shape)\n",
    "\n",
    "S_t_mat_1 = np.sum(np.multiply(Psi_1_aux_1, Psi_2_aux_1), axis=2) \n",
    "print(S_t_mat.shape, S_t_mat_1.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "del Psi_1_aux, Psi_2_aux, Psi_1_aux_1, Psi_2_aux_1, data_mat_swap_idx,data_mat_swap_idx_1, A_2, A_2_1 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vector $\\vec W_t$ could be solved by\n",
    "\n",
    "$$\\vec W_t=\\mathbf S_t^{-1}\\mathbf M_t$$\n",
    "\n",
    "where $\\mathbf S_t$ and $\\mathbf M_t$ are matrix and vector respectively with elements given by\n",
    "\n",
    "$$S_{nm}^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Psi_n\\left(X_t^k,a_t^k\\right)\\Psi_m\\left(X_t^k,a_t^k\\right)}\\quad\\quad M_n^{\\left(t\\right)}=\\sum_{k=1}^{N_{MC}}{\\Psi_n\\left(X_t^k,a_t^k\\right)\\left(R_t\\left(X_t,a_t,X_{t+1}\\right)+\\gamma\\max_{a_{t+1}\\in\\mathcal{A}}Q_{t+1}^\\star\\left(X_{t+1},a_{t+1}\\right)\\right)}$$\n",
    "\n",
    "Define function *function_S* and *function_M* to compute the value of matrix $\\mathbf S_t$ and vector $\\mathbf M_t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# vectorized functions\n",
    "\n",
    "def function_S_vec(t,S_t_mat,reg_param):\n",
    "    # Compute the matrix S_{nm} from Eq. (75) (with a regularization!)\n",
    "    S_mat = S_t_mat[:,:,t]     \n",
    "    S_mat_reg = S_mat + reg_param * np.eye(S_mat.shape[0])\n",
    "    return S_mat_reg\n",
    "\n",
    "# this function requires some refinement!\n",
    "def function_M_vec(t,\n",
    "                   Q_star, # max_Q_star, \n",
    "                   R, \n",
    "                   Psi_mat_t,  # 2D array of dimension 3M x num_MC \n",
    "                   gamma=gamma):\n",
    "    \n",
    "    # Psi_mat = Psi_mat_t[:,:,t]   # 2D array of dimension 3M x num_MC \n",
    "    tmp = R.loc[:,t] + gamma * Q_star.iloc[:,t+1]\n",
    "    M_t = np.dot(Psi_mat_t, tmp.values)\n",
    "    return M_t\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call *function_S* and *function_M* for $t=T-1,...,0$ together with vector $\\vec\\Psi\\left(X_t,a_t\\right)$ to compute $\\vec W_t$ and learn the Q-function $Q_t^\\star\\left(X_t,a_t\\right)=\\mathbf A_t^T\\mathbf U_W\\left(t,X_t\\right)$ implied by the input data backward recursively with terminal condition $Q_T^\\star\\left(X_T,a_T=0\\right)=-\\Pi_T\\left(X_T\\right)-\\lambda Var\\left[\\Pi_T\\left(X_T\\right)\\right]$.\n",
    "\n",
    "When the vector $ \\vec{W}_t $ is computed as per the above at time $ t $, \n",
    "we can convert it back to a matrix $ \\bf{W}_t $ obtained from the vector $ \\vec{W}_t $ by \n",
    "reshaping to the shape $ 3 \\times M $.\n",
    "\n",
    "We can now calculate the matrix $ {\\bf U}_t $\n",
    "at time $ t $ for the whole set of MC paths as follows (this is Eq.(65) from the paper in a matrix form):\n",
    "\n",
    "$$  \\mathbf U_{W} \\left(t,X_t \\right) = \n",
    "\\left[\\begin{matrix} \\mathbf U_W^{0,k}\\left(t,X_t \\right) \\\\  \n",
    "\\mathbf U_W^{1,k}\\left(t,X_t \\right) \\\\ \\mathbf U_W^{2,k} \\left(t,X_t \\right)\n",
    "\\end{matrix}\\right]\n",
    "= \\bf{W}_t \\Phi_t \\left(t,X_t \\right)  $$\n",
    "\n",
    "Here the matrix $ {\\bf \\Phi}_t $ has the shape shape $ M \\times N_{MC}$. \n",
    "Therefore, their dot product has dimension $ 3 \\times N_{MC}$, as it should be. \n",
    "\n",
    "Once this matrix $ {\\bf U}_t $ is computed, individual vectors $ {\\bf U}_{W}^{1}, {\\bf U}_{W}^{2}, {\\bf U}_{W}^{3} $ for all MC paths are read off as rows of this matrix.\n",
    "\n",
    "From here, we can compute the optimal action and optimal Q-function $Q^{\\star}(X_t, a_t^{\\star}) $ at the optimal action for a given step $ t $. This will be used to evaluate the $ \\max_{a_{t+1} \\in \\mathcal{A}} Q^{\\star} \\left(X_{t+1}, a_{t+1} \\right) $.\n",
    "\n",
    "\n",
    "The optimal action and optimal Q-function with the optimal action could be computed by\n",
    "\n",
    "$$a_t^\\star\\left(X_t\\right)=\\frac{\\mathbb{E}_{t} \\left[  \\Delta \\hat{S}_{t}  \\hat{\\Pi}_{t+1} + \\frac{1}{2 \\gamma \\lambda} \\Delta S_{t} \\right]}{\n",
    "  \\mathbb{E}_{t} \\left[ \\left( \\Delta \\hat{S}_{t} \\right)^2 \\right]}\\, , \n",
    "\\quad\\quad Q_t^\\star\\left(X_t,a_t^\\star\\right)=\\mathbf U_W^{\\left(0\\right)}\\left(t,X_t\\right)+ a_t^\\star \\mathbf U_W^{\\left(2\\right)}\\left(t,X_t\\right) +\\frac{1}{2}\\left(a_t^\\star\\right)^2\\mathbf U_W^{\\left(2\\right)}\\left(t,X_t\\right)$$\n",
    "\n",
    "with terminal condition $a_T^\\star=0$ and $Q_T^\\star\\left(X_T,a_T^\\star=0\\right)=-\\Pi_T\\left(X_T\\right)-\\lambda Var\\left[\\Pi_T\\left(X_T\\right)\\right]$.\n",
    "\n",
    "Plots of 5 optimal action $a_t^\\star\\left(X_t\\right)$, optimal Q-function with optimal action $Q_t^\\star\\left(X_t,a_t^\\star\\right)$ and implied Q-function $Q_t^\\star\\left(X_t,a_t\\right)$ paths are shown below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitted Q Iteration (FQI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Time Cost: 0.6679928302764893 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "starttime = time.time()\n",
    "\n",
    "# implied Q-function by input data (using the first form in Eq.(68))\n",
    "Q_RL = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Q_RL.iloc[:,-1] = - Pi.iloc[:,-1] - risk_lambda * np.var(Pi.iloc[:,-1])\n",
    "\n",
    "# similar variables for the twin dataset:\n",
    "Q_RL_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Q_RL_1.iloc[:,-1] = - Pi_1.iloc[:,-1] - risk_lambda * np.var(Pi_1.iloc[:,-1])\n",
    "\n",
    "# optimal action\n",
    "a_opt = np.zeros((N_MC,T+1))\n",
    "a_star = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "a_star.iloc[:,-1] = 0\n",
    "\n",
    "# optimal action\n",
    "a_opt_1 = np.zeros((N_MC,T+1))\n",
    "a_star_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "a_star_1.iloc[:,-1] = 0\n",
    "\n",
    "# optimal Q-function with optimal action\n",
    "Q_star = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Q_star.iloc[:,-1] = Q_RL.iloc[:,-1]\n",
    "\n",
    "# optimal Q-function with optimal action\n",
    "Q_star_1 = pd.DataFrame([], index=range(1, N_MC+1), columns=range(T+1))\n",
    "Q_star_1.iloc[:,-1] = Q_RL_1.iloc[:,-1]\n",
    "\n",
    "max_Q_star = np.zeros((N_MC,T+1))\n",
    "max_Q_star[:,-1] = Q_RL.iloc[:,-1].values\n",
    "\n",
    "max_Q_star_1 = np.zeros((N_MC,T+1))\n",
    "max_Q_star_1[:,-1] = Q_RL_1.iloc[:,-1].values\n",
    "\n",
    "num_basis = data_mat_t.shape[2]\n",
    "\n",
    "reg_param = 1e-3\n",
    "hyper_param =  1e-1\n",
    "\n",
    "# The backward loop\n",
    "for t in range(T-1, -1, -1):\n",
    "    # calculate vector W_t\n",
    "    S_mat_reg = function_S_vec(t,S_t_mat,reg_param) \n",
    "    M_t = function_M_vec(t,Q_star, R, Psi_mat[:,:,t], gamma)\n",
    "    W_t = np.dot(np.linalg.inv(S_mat_reg),M_t)  # this is an 1D array of dimension 3M\n",
    "    \n",
    "    # reshape to a matrix W_mat  \n",
    "    W_mat = W_t.reshape((3, num_basis), order='F')  # shape 3 x M \n",
    "        \n",
    "    # make matrix Phi_mat\n",
    "    Phi_mat = data_mat_t[t,:,:].T  # dimension M x N_MC\n",
    "\n",
    "    # compute matrix U_mat of dimension N_MC x 3 \n",
    "    U_mat = np.dot(W_mat, Phi_mat)\n",
    "    \n",
    "    # twin variables for the twin dataset:\n",
    "    S_mat_reg_1 = function_S_vec(t,S_t_mat_1,reg_param) \n",
    "    M_t_1 = function_M_vec(t,Q_star_1, R_1, Psi_mat_1[:,:,t], gamma)\n",
    "    W_t_1 = np.dot(np.linalg.inv(S_mat_reg_1),M_t_1)  # this is an 1D array of dimension 3M\n",
    "    \n",
    "    # reshape to a matrix W_mat  \n",
    "    W_mat_1 = W_t_1.reshape((3, num_basis), order='F')  # shape 3 x M \n",
    "        \n",
    "    # make matrix Phi_mat\n",
    "    Phi_mat_1 = data_mat_t_1[t,:,:].T  # dimension M x N_MC\n",
    "\n",
    "    # compute matrix U_mat_1 of dimension N_MC x 3 \n",
    "    U_mat_1 = np.dot(W_mat_1, Phi_mat_1)\n",
    "    \n",
    "    # compute vectors U_W^0,U_W^1,U_W^2 as rows of matrix U_mat  \n",
    "    U_W_0 = U_mat[0,:]\n",
    "    U_W_1 = U_mat[1,:]\n",
    "    U_W_2 = U_mat[2,:]\n",
    "    \n",
    "    U_W_0_1 = U_mat_1[0,:]\n",
    "    U_W_1_1 = U_mat_1[1,:]\n",
    "    U_W_2_1 = U_mat_1[2,:]\n",
    "     \n",
    "    # IMPORTANT!!! Instead, use hedges computed as in DP approach:\n",
    "    # in this way, errors of function approximation do not back-propagate. \n",
    "    # This provides a stable solution, unlike\n",
    "    # the first method that leads to a diverging solution \n",
    "    A_mat = function_A_vec(t,delta_S_hat,data_mat_t,reg_param)\n",
    "    B_vec = function_B_vec(t, Pi_hat)\n",
    "    phi = np.dot(np.linalg.inv(A_mat), B_vec)\n",
    "    \n",
    "    A_mat_1 = function_A_vec(t,delta_S_hat_1,data_mat_t_1,reg_param)\n",
    "    B_vec_1 = function_B_vec(t, Pi_hat_1)\n",
    "\n",
    "    phi_1 = np.dot(np.linalg.inv(A_mat_1), B_vec_1)\n",
    "    \n",
    "    a_opt[:,t] = np.dot(data_mat_t[t,:,:],phi)\n",
    "    a_star.loc[:,t] = a_opt[:,t] \n",
    "    \n",
    "    a_opt_1[:,t] = np.dot(data_mat_t_1[t,:,:],phi_1)\n",
    "    a_star_1.loc[:,t] = a_opt_1[:,t] \n",
    "    \n",
    "    max_Q_star[:,t] = U_W_0 + a_opt[:,t] * U_W_1 + 0.5 * (a_opt[:,t]**2) * U_W_2 \n",
    "    max_Q_star_1[:,t] = U_W_0_1 + a_opt_1[:,t] * U_W_1_1 + 0.5 * (a_opt_1[:,t]**2) * U_W_2_1 \n",
    "      \n",
    "    # update dataframes     \n",
    "    Q_star.loc[:,t] = max_Q_star[:,t]\n",
    "    \n",
    "    # update the Q_RL solution given by a dot product of two matrices W_t Psi_t\n",
    "    Psi_t = Psi_mat[:,:,t].T  # dimension N_MC x 3M  \n",
    "    Q_RL.loc[:,t] = np.dot(Psi_t, W_t)\n",
    "    \n",
    "    a_star_1.loc[:,t] = a_opt_1[:,t] \n",
    "    Q_star_1.loc[:,t] = max_Q_star_1[:,t]\n",
    "    \n",
    "    # update the Q_RL solution given by a dot product of two matrices W_t Psi_t\n",
    "    Psi_t_1 = Psi_mat_1[:,:,t].T  # dimension N_MC x 3M  \n",
    "    Q_RL_1.loc[:,t] = np.dot(Psi_t_1, W_t_1)\n",
    "    \n",
    "    # trim outliers for Q_RL\n",
    "    up_percentile_Q_RL =  95 # 95\n",
    "    low_percentile_Q_RL = 5 # 5\n",
    "    \n",
    "    low_perc_Q_RL, up_perc_Q_RL = np.percentile(Q_RL.loc[:,t],[low_percentile_Q_RL,up_percentile_Q_RL])\n",
    "    \n",
    "    # trim outliers in values of max_Q_star:\n",
    "    flag_lower = Q_RL.loc[:,t].values < low_perc_Q_RL\n",
    "    flag_upper = Q_RL.loc[:,t].values > up_perc_Q_RL\n",
    "    Q_RL.loc[flag_lower,t] = low_perc_Q_RL\n",
    "    Q_RL.loc[flag_upper,t] = up_perc_Q_RL\n",
    "    \n",
    "    low_perc_Q_RL_1, up_perc_Q_RL_1 = np.percentile(Q_RL_1.loc[:,t],[low_percentile_Q_RL,up_percentile_Q_RL])\n",
    "   \n",
    "    # trim outliers in values of max_Q_star:\n",
    "    flag_lower_1 = Q_RL_1.loc[:,t].values < low_perc_Q_RL_1\n",
    "    flag_upper_1 = Q_RL_1.loc[:,t].values > up_perc_Q_RL_1\n",
    "    Q_RL_1.loc[flag_lower_1,t] = low_perc_Q_RL_1\n",
    "    Q_RL_1.loc[flag_upper_1,t] = up_perc_Q_RL_1\n",
    "    \n",
    "endtime = time.time()\n",
    "print('\\nTime Cost:', endtime - starttime, 'seconds')\n",
    "\n",
    "f, axarr = plt.subplots(3, 2)\n",
    "f.subplots_adjust(hspace=.5)\n",
    "f.set_figheight(8.0)\n",
    "f.set_figwidth(8.0)\n",
    "\n",
    "step_size = N_MC // 10\n",
    "idx_plot = np.arange(step_size, N_MC, step_size)\n",
    "axarr[0, 0].plot(a_star.T.iloc[:, idx_plot]) \n",
    "axarr[0, 0].set_xlabel('Time Steps')\n",
    "axarr[0, 0].set_title(r'Optimal action $a_t^{\\star}$')\n",
    "\n",
    "axarr[0, 1].plot(a_star_1.T.iloc[:, idx_plot]) \n",
    "axarr[0, 1].set_xlabel('Time Steps')\n",
    "axarr[0, 1].set_title(r'Optimal action $a_t^{\\star}$')\n",
    "\n",
    "axarr[1, 0].plot(Q_RL.T.iloc[:, idx_plot]) \n",
    "axarr[1, 0].set_xlabel('Time Steps')\n",
    "axarr[1, 0].set_title(r'Q-function $Q_t^{\\star} (X_t, a_t)$')\n",
    "\n",
    "axarr[1, 1].plot(Q_RL_1.T.iloc[:, idx_plot]) \n",
    "axarr[1, 1].set_xlabel('Time Steps')\n",
    "axarr[1, 1].set_title(r'Q-function $Q_t^{\\star}(X_t, a_t)$')\n",
    "\n",
    "axarr[2, 0].plot(Q_star.T.iloc[:, idx_plot]) \n",
    "axarr[2, 0].set_xlabel('Time Steps')\n",
    "axarr[2, 0].set_title(r'Optimal Q-function $Q_t^{\\star} (X_t, a_t^{\\star})$') \n",
    "\n",
    "axarr[2, 1].plot(Q_star_1.T.iloc[:, idx_plot]) \n",
    "axarr[2, 1].set_xlabel('Time Steps')\n",
    "axarr[2, 1].set_title(r'Optimal Q-function $Q_t^{\\star} (X_t, a_t^{\\star})$')\n",
    "\n",
    "plt.savefig('QLBS_FQI_off_policy_summary_ATM_eta_%d.png' % (100 * eta), dpi=600);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the optimal action $a_t^\\star\\left(X_t\\right)$ and optimal Q-function with optimal action $Q_t^\\star\\left(X_t,a_t^\\star\\right)$ given by Dynamic Programming and Reinforcement Learning.\n",
    "\n",
    "Plots of 1 path comparisons are given below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot a and a_star\n",
    "# plot 1 path\n",
    "\n",
    "num_path =  120\n",
    "\n",
    "# Note that a from the DP method and a_star from the RL method are now identical by construction\n",
    "plt.plot(a.T.iloc[:,num_path], label=\"DP Action\")\n",
    "plt.plot(a_star.T.iloc[:,num_path], label=\"RL Action\")\n",
    "plt.legend()\n",
    "plt.xlabel('Time Steps')\n",
    "plt.title('Optimal Action Comparison Between DP and RL')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary of the RL-based pricing with QLBS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------\n",
      "       QLBS RL Option Pricing       \n",
      "---------------------------------\n",
      "\n",
      "Initial Stock Price:      100\n",
      "Drift of Stock:           0.05\n",
      "Volatility of Stock:      0.15\n",
      "Risk-free Rate:           0.03\n",
      "Risk aversion parameter : 0.001\n",
      "Strike:                   100\n",
      "Maturity:                 1\n",
      "\n",
      "The QLBS Put Price 1 :    4.3806\n",
      "\n",
      "The QLBS Put Price 2 :    6.6631\n",
      "QLBS Put Price:             5.5218 +/- 1.1412 \n",
      "\n",
      "Black-Sholes Put Price:   4.5296\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# QLBS option price\n",
    "C_QLBS = - Q_star.copy()\n",
    "C_QLBS_1 = - Q_star_1.copy()\n",
    "\n",
    "print('---------------------------------')\n",
    "print('       QLBS RL Option Pricing       ')\n",
    "print('---------------------------------\\n')\n",
    "print('%-25s' % ('Initial Stock Price:'), S0)\n",
    "print('%-25s' % ('Drift of Stock:'), mu)\n",
    "print('%-25s' % ('Volatility of Stock:'), sigma)\n",
    "print('%-25s' % ('Risk-free Rate:'), r)\n",
    "print('%-25s' % ('Risk aversion parameter :'), risk_lambda)\n",
    "print('%-25s' % ('Strike:'), K)\n",
    "print('%-25s' % ('Maturity:'), M)\n",
    "print('%-26s %.4f' % ('\\nThe QLBS Put Price 1 :', (np.mean(C_QLBS.iloc[:,0]))))\n",
    "print('%-26s %.4f' % ('\\nThe QLBS Put Price 2 :', (np.mean(C_QLBS_1.iloc[:,0]))))\n",
    "\n",
    "\n",
    "QLBS_prices = np.array([C_QLBS.iloc[0,0],C_QLBS_1.iloc[0,0]])\n",
    "mean_price = np.mean(QLBS_prices)\n",
    "std_price = np.std(QLBS_prices)\n",
    "\n",
    "print('%-26s  %.4f +/- %.4f ' % ('QLBS Put Price: ',mean_price,std_price ))\n",
    "print('%-26s %.4f' % ('\\nBlack-Sholes Put Price:', bs_put(0)))\n",
    "print('\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# add here calculation of different MC runs (6 repetitions of action randomization)\n",
    "\n",
    "# on-policy values\n",
    "y1_onp = 5.0211 # 4.9170\n",
    "y2_onp = 4.7798 # 7.6500\n",
    "\n",
    "# QLBS_price_on_policy = 4.9004 +/- 0.1206\n",
    "\n",
    "# these are the results for noise eta = 0.15\n",
    "# p1 = np.array([5.0174, 4.9249, 4.9191, 4.9039, 4.9705, 4.6216 ])\n",
    "# p2 = np.array([6.3254, 8.6733, 8.0686, 7.5355, 7.1751, 7.1959 ])\n",
    "\n",
    "p1 = np.array([5.0485, 5.0382, 5.0211, 5.0532, 5.0184])\n",
    "p2 = np.array([4.7778, 4.7853, 4.7781,4.7805, 4.7828])\n",
    "\n",
    "# results for eta = 0.25\n",
    "# p3 = np.array([4.9339, 4.9243, 4.9224, 5.1643, 5.0449, 4.9176 ])\n",
    "# p4 = np.array([7.7696,8.1922, 7.5440,7.2285, 5.6306, 12.6072])\n",
    "\n",
    "p3 = np.array([5.0147, 5.0445, 5.1047, 5.0644, 5.0524])\n",
    "p4 = np.array([4.7842,4.7873, 4.7847, 4.7792, 4.7796])\n",
    "\n",
    "# eta = 0.35 \n",
    "# p7 = np.array([4.9718, 4.9528, 5.0170, 4.7138, 4.9212, 4.6058])\n",
    "# p8 = np.array([8.2860, 7.4012, 7.2492, 8.9926, 6.2443, 6.7755])\n",
    "\n",
    "p7 = np.array([5.1342, 5.2288, 5.0905, 5.0784, 5.0013 ])\n",
    "p8 = np.array([4.7762, 4.7813,4.7789, 4.7811, 4.7801])\n",
    "\n",
    "# results for eta = 0.5\n",
    "# p5 = np.array([4.9446, 4.9894,6.7388, 4.7938,6.1590, 4.5935 ])\n",
    "# p6 = np.array([7.5632, 7.9250, 6.3491, 7.3830, 13.7668, 14.6367 ])\n",
    "\n",
    "p5 = np.array([3.1459, 4.9673, 4.9348, 5.2998, 5.0636 ])\n",
    "p6 = np.array([4.7816, 4.7814, 4.7834, 4.7735, 4.7768])\n",
    "x = np.array([0.15, 0.25, 0.35, 0.5])\n",
    "y1 = np.array([np.mean(p1), np.mean(p3), np.mean(p7), np.mean(p5)])\n",
    "y2 = np.array([np.mean(p2), np.mean(p4), np.mean(p8), np.mean(p6)])\n",
    "y_err_1 = np.array([np.std(p1), np.std(p3),np.std(p7),  np.std(p5)])\n",
    "y_err_2 = np.array([np.std(p2), np.std(p4), np.std(p8), np.std(p6)])\n",
    "\n",
    "# plot it \n",
    "f, axs = plt.subplots(nrows=2, ncols=2, sharex=True)\n",
    "\n",
    "f.subplots_adjust(hspace=.5)\n",
    "f.set_figheight(6.0)\n",
    "f.set_figwidth(8.0)\n",
    "\n",
    "ax = axs[0,0]\n",
    "ax.plot(x, y1)\n",
    "ax.axhline(y=y1_onp,linewidth=2, color='r')\n",
    "textstr = 'On-policy value = %2.2f'% (y1_onp)\n",
    "props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)                      \n",
    "# place a text box in upper left in axes coords\n",
    "ax.text(0.05, 0.15, textstr, fontsize=11,transform=ax.transAxes, verticalalignment='top', bbox=props)\n",
    "ax.set_title('Mean option price')\n",
    "ax.set_xlabel('Noise level')\n",
    "\n",
    "ax = axs[0,1]\n",
    "ax.plot(x, y2)\n",
    "ax.axhline(y=y2_onp,linewidth=2, color='r')\n",
    "textstr = 'On-policy value = %2.2f'% (y2_onp)\n",
    "props = dict(boxstyle='round', facecolor='wheat', alpha=0.5)     \n",
    "\n",
    "# place a text box in upper left in axes coords\n",
    "ax.text(0.35, 0.95, textstr, fontsize=11,transform=ax.transAxes, verticalalignment='top', bbox=props)\n",
    "ax.set_title('Mean option price')\n",
    "ax.set_xlabel('Noise level')\n",
    "\n",
    "ax = axs[1,0]\n",
    "ax.plot(x, y_err_1)\n",
    "ax.set_title('Std of option price')\n",
    "ax.set_xlabel('Noise level')\n",
    "\n",
    "ax = axs[1,1]\n",
    "ax.plot(x, y_err_2)\n",
    "ax.set_title('Std of option price')\n",
    "ax.set_xlabel('Noise level')\n",
    "\n",
    "f.suptitle('Mean and std of option price vs noise level')\n",
    "\n",
    "plt.savefig('Option_price_vs_noise_level.png', dpi=600);"
   ]
  }
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